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As indicated earlier, the matter of the aforementioned unacceptable negative depth has been addressed in detail and satisfactorily treated here, as will be seen in the "Formulation of the inverse problem and the proposed steps of its solving" section.
Note that, as has been discussed in the "Formulation of the inverse problem and the proposed steps of its solving" section, the SD method was applied to the abovementioned SP profile.
Note that both the occasional negativity of the inverse model parameters and the effect of the initial guess on the convergence are satisfactorily addressed and treated here as will be seen in the "Formulation of the inverse problem and the proposed steps of its solving" and "Model 1" sections.
Jagannadha Rao et al. (1993) performed the Marquardt inversion in the space of the model parameters themselves (h, a, θ, and k), which does not force the positivity of these parameters as will be seen and discussed in the "Formulation of the inverse problem and the proposed steps of its solving" and "Model 1" sections below.
This assures that the inversion scheme always produces geologically acceptable and meaningful inverse results (that is, the body never virtually extends in the air), as will be discussed in the "Formulation of the inverse problem and the proposed steps of its solving" section.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com